PaperlayerView exact revision on arXiv

Source-linked AI summary

Massive MIMO performance evaluation based on measured propagation data

Xiang Gao, Ove Edfors, Fredrik Rusek, Fredrik Tufvesson

arXiv:1403.3376v3cs.IT

TL;DR

Massive MIMO promises high multi-user capacity, but much of its evidence comes from idealized i.i.d. Rayleigh channels. This paper measures 128-port UCA and virtual ULA channels at 2.6 GHz across three propagation conditions and finds performance close to the Rayleigh reference in several scenarios, with a remaining gap in closely located strong-LOS conditions.

  • Problem

    The paper asks whether massive MIMO's theoretical advantages persist in real propagation environments and practical antenna-array setups rather than only i.i.d. Rayleigh channels.

  • Method

    The study measures outdoor-to-outdoor channels using 128-port UCA and virtual ULA arrays, evaluates three user-placement and propagation scenarios, and analyzes orthogonality and sum-rate capacity.

  • Results

    In NLOS and far-separated LOS scenarios, both arrays achieve performance close to i.i.d. Rayleigh channels; in closely located strong-LOS conditions, the ULA and UCA reach 90% and 75% of asymptotic capacity above 40 antennas.

  • Takeaways & Limitations

    The measured real channels contain characteristics that allow efficient massive MIMO use, so theoretical advantages can also be obtained in real channels.

Abstract

from arXiv · show

Massive MIMO, also known as very-large MIMO or large-scale antenna systems, is a new technique that potentially can offer large network capacities in multi-user scenarios. With a massive MIMO system, we consider the case where a base station equipped with a large number of antenna elements simultaneously serves multiple single-antenna users in the same time-frequency resource. So far, investigations are mostly based on theoretical channels with independent and identically distributed (i.i.d.) complex Gaussian coefficients, i.e., i.i.d. Rayleigh channels. Here, we investigate how massive MIMO performs in channels measured in real propagation environments. Channel measurements were performed at 2.6 GHz using a virtual uniform linear array (ULA) which has a physically large aperture, and a practical uniform cylindrical array (UCA) which is more compact in size, both having 128 antenna ports. Based on measurement data, we illustrate channel behavior of massive MIMO in three representative propagation conditions, and evaluate the corresponding performance. The investigation shows that the measured channels, for both array types, allow us to achieve performance close to that in i.i.d. Rayleigh channels. It is concluded that in real propagation environments we have characteristics that can allow for efficient use of massive MIMO, i.e., the theoretical advantages of this new technology can also be harvested in real channels.

I. INTRODUCTION

The introduction motivates testing massive MIMO beyond idealized i.i.d. Rayleigh channels by measuring performance in real propagation environments with practical large arrays.

  • Massive MIMO uses tens to hundreds of base-station antennas to serve multiple single-antenna users in the same time-frequency resource.
  • Theory predicts gains in link reliability, spectral efficiency, transmit energy efficiency, and reduced intra-cell interference under favorable propagation.Favorable propagation corresponds to increasingly orthogonal user channels, enabling simple linear precoding and detection schemes to approach optimality.
  • Prior investigations largely rely on i.i.d. complex Gaussian channels and antenna numbers that grow without limit, motivating validation with practical arrays and real propagation.
  • This paper measures outdoor-to-outdoor channels with 128-port UCA and virtual ULA arrays across closely located LOS, closely located NLOS, and far-separated-user scenarios.
  • The UCA is more compact and resolves incoming waves in two dimensions, whereas the larger ULA offers higher angular resolution in one dimension but may exhibit different performance.
  • The study evaluates measured-channel behavior and performance using singular value spread and sum-rate capacity across the investigated propagation scenarios.

A. Measurement setups

The study compares two 128-port base-station arrays measured at 2.6 GHz in a semi-urban outdoor environment, while accounting for practical deployment and coupling differences.

  • The compact UCA has 64 dual-polarized patch antennas and 128 ports, while the virtual ULA uses 128 vertically polarized omni-directional antenna positions.The UCA is approximately 30 cm in diameter and height; the ULA is synthesized by moving one antenna along a rail.
  • Both arrays use half-wavelength element spacing and operate in the 2.6 GHz range, with measurements recorded over 50 MHz bandwidth.
  • The virtual ULA campaign required about half an hour per measurement, so measurements were performed at night to keep the channel as static as possible.Repeated measurements had average amplitude correlation coefficients between 0.95 and 0.99.
  • The compact UCA has worst-case neighboring-element mutual coupling of -11 dB, whereas the virtual ULA experiences no mutual coupling effect.The paper notes that coupling can affect massive MIMO performance and that practical coupling studies remain needed.
  • Measurements placed both base-station arrays on the E-building roof and moved a single omni-directional antenna among eight user measurement sites.The sites included LOS and NLOS conditions, with one site having different LOS visibility for the two arrays because of mounting height.

III. SYSTEM DESCRIPTION

The paper models a narrow-band MU-MIMO downlink using measured channel matrices, explicit normalization procedures, and fixed interference-free user SNR for fair antenna-count comparisons.

  • The system has N OFDM subcarriers, an M-antenna base station, and K single-antenna users served simultaneously with perfect channel state information.The channel is treated as narrow-band at each OFDM subcarrier.
  • At each subcarrier, the downlink model maps a normalized transmit vector through the K×M channel matrix to received user signals plus complex Gaussian noise.The transmit-energy factor ρK/M increases with users and decreases with base-station antennas.
  • As the antenna count increases, the array gain is used to reduce transmit power rather than increase users' receive SNR.The model keeps a constant interference-free SNR ρ to support fair and realistic comparisons.
  • Measured data from selected user positions form a K×128 raw channel matrix, from which M antenna columns are selected after normalization.
  • Normalization 1 removes average channel-attenuation imbalance between users while retaining variations across antenna elements and frequencies.
  • Normalization 2 preserves differences in user attenuation and variations over antenna elements and frequencies using unit average energy over ports, users, and subcarriers.Both normalizations are applied before selecting antenna subsets, preserving array power imbalance.

B. Singular value spread

Singular value spread measures how well user channels are jointly orthogonal and therefore spatially separable. Massive MIMO is expected to reduce and stabilize this spread as the antenna count becomes much larger than the user count.

  • Singular value spread evaluates joint orthogonality by comparing the largest and smallest singular values of the normalized propagation matrix.It is derived from the singular values in the matrix’s singular value decomposition.
  • A large κ_ℓ indicates that at least two user-channel vectors are nearly parallel and difficult to separate spatially.By contrast, κ_ℓ = 1, or 0 dB, represents pairwise orthogonal user channels.
  • The singular value spread indicates whether users should share a time-frequency resource and is closely connected to MIMO precoder and detector performance.
  • As M grows much larger than K, user channels are expected to become more orthogonal, producing smaller and more stable singular value spreads.Greater stability can help avoid bad channel conditions and stabilize MIMO precoders and detectors.

C. Dirty-paper coding capacity

The capacity analysis evaluates dirty-paper coding sum-rate in measured multi-user channels while accounting for power allocation and channel attenuation. It compares the measured channels with the interference-free capacity approached by i.i.d. Rayleigh channels.

  • Sum-rate capacity quantifies overall MU-MIMO performance beyond the minimum-user-quality indication provided by singular value spread.A small singular value spread is associated with high capacity because user interference is reduced.
  • Dirty-paper coding achieves the narrow-band MU-MIMO downlink sum-rate capacity by optimizing transmit-power allocation across user channels.The diagonal power-allocation matrix is optimized under a total transmit-power constraint, using iterative water-filling.
  • Far-apart users can exhibit strong attenuation differences, causing capacity optimization to allocate disproportionate power to weaker users and potentially reduce multi-user transmission to one dominant user.
  • Because limited measurement positions prevent analyzing grouped users with similar attenuation, the evaluation removes far-user attenuation imbalance and retains co-located-user attenuation variations as specified by two normalizations.
  • The interference-free capacity is the asymptotic benchmark approached by i.i.d. Rayleigh channels as the antenna count grows, and the measured channels are evaluated by their fraction of this benchmark.

IV. PROPAGATION CHARACTERISTICS

The measured propagation scenarios reveal how array aperture, user spacing, and LOS/NLOS conditions shape spatial separability. Distinct fingerprints generally indicate better separation, while overlapping fingerprints signal greater correlation and require quantitative evaluation of amplitude and phase effects.

  • Scenario setup: The study examines four-user cases with 1.5–2 m spacing for co-located users and more than 10 m spacing for far-apart users across LOS and NLOS conditions.The scenarios are co-located LOS, co-located NLOS, and far-apart LOS users.
  • Fingerprint construction: Spatial fingerprints summarize where 90% of each user’s received energy is concentrated across the ULA, using APS estimates derived with the SAGE algorithm.The UCA samples the propagation channel at the beginning of the ULA through differently oriented patch antennas.
  • LOS co-located users: Co-located LOS users have overlapping fingerprints concentrated near 160 degrees, indicating high channel correlation and potentially difficult spatial separation.Scatterer energy around 20 degrees and amplitude or phase differences may still improve separability beyond the fingerprint view.
  • NLOS co-located users: Co-located NLOS users in rich scattering have complex, distinct fingerprints distributed across a much larger angular range, indicating lower spatial correlation and better expected separation.
  • LOS far-apart users: Far-apart LOS users generally have different fingerprints and are expected to separate well, although ULA angular ambiguity can make two users appear to arrive from the same direction.The later evaluation shows that those users can nevertheless be spatially separated.
  • Array effects: The physically large ULA provides greater spatial variation and can decorrelate closely located users instantaneously, whereas the compact UCA sees only part of the propagation channel and may separate signals less effectively.Strong LOS and narrowly directed energy can make UCA patch antennas contribute little to separating co-located users.

V. PERFORMANCE EVALUATION

The performance evaluation compares singular value spreads and sum-rate capacities in measured channels, first for four users and then for sixteen simultaneously served users.

  • The evaluation uses singular value spread and sum-rate capacity to quantify performance for K = 4 and K = 16 users.

A. Four users (K =4)

The evaluation uses 128 measured antenna ports, sampling antenna subsets and subcarriers to assess singular-value spread and DPC capacity. For i.i.d. Rayleigh channels, increasing antennas sharply improves singular-value behavior and stability.

  • A. Four users (K =4): 128 antenna ports are evaluated through 161 subcarriers and 2000 random selections of M antennas, with M ranging from 4 to 128.The evaluation reports CDFs of singular value spreads and average DPC capacities with 90% confidence intervals.
  • A. Four users (K =4): For i.i.d. Rayleigh channels, the median singular value spread falls from 17 dB to below 4 dB as antennas increase from 4 to 32 and 128.The CDFs also lose substantial upper tails, indicating more stable singular-value spreads at larger array sizes.

1) Four users co-located with LOS:

With four closely located LOS users, measured channels have worse orthogonality than i.i.d. Rayleigh channels, but larger arrays improve and stabilize spatial separation. DPC capacity nevertheless reaches substantial fractions of the Rayleigh reference.

  • 1) Four users co-located with LOS:: Measured ULA and UCA channels have significantly larger singular value spreads than i.i.d. Rayleigh channels for 4, 32, and 128 antennas.The difference is attributed in the passage to co-location and strong LOS conditions.
  • 1) Four users co-located with LOS:: 14 dB and 12 dB median singular-value-spread reductions occur for the ULA and UCA, respectively, as antennas increase from 4 to 128.Upper tails nearly disappear at 128 antennas, while orthogonality becomes more stable across antenna selections and subcarriers.
  • 1) Four users co-located with LOS:: 90% and 75% of asymptotic i.i.d. Rayleigh capacity are achieved by the ULA and UCA, respectively, above 40 antennas.Above 40 antennas corresponds to using ten times the number of users in this four-user scenario.
  • 1) Four users co-located with LOS:: The i.i.d. Rayleigh reference reaches an asymptotic downlink DPC capacity of 13.8 bps/Hz, with decreasing capacity variation as antennas increase.Measured-channel averages are lower and variations are larger in this scenario.

2) Four users co-located with NLOS:

Across the measured scenarios, NLOS scattering and user separation improve channel orthogonality and DPC capacity, while array geometry and practical precoding affect performance and variability. The ULA generally performs better, but the UCA benefits when users are distributed around the base station.

  • 2) Four users co-located with NLOS:: In co-located NLOS conditions, the ULA performs very close to asymptotic i.i.d. Rayleigh capacity and the UCA exceeds 90% above 40 antennas.The passage links these capacity gains to rich scattering and improved spatial separation.
  • 3) Four users located far from each other with LOS:: For well-separated LOS users, the ULA again performs very close to i.i.d. Rayleigh channels, while the UCA’s median spread falls below 5 dB at 128 antennas.Measured-channel singular value spreads become stable with a large number of antennas.
  • 3) Four users located far from each other with LOS:: Both arrays perform very close to asymptotic i.i.d. Rayleigh capacity above 40 antennas in the well-separated LOS scenario, with slightly lower UCA performance.The increased inter-user spacing produces reasonably different spatial fingerprints.
  • Array comparison: The ULA generally outperforms the UCA because its large aperture provides greater spatial variation and angular resolution, while the UCA performs better when users are well distributed around the base station.The UCA can separate scatterers at different azimuth angles in that placement.
  • Capacity variation and practical precoding: Measured-channel capacity variations are larger and decrease more slowly than in i.i.d. Rayleigh channels because of stronger power variations across antenna elements and frequencies.With practical ZF and MF precoding, sum-rate converges more slowly, requiring more antennas; serving more users also requires more antennas.

B. Sixteen users (K =16)

With sixteen users, increasing the antenna count improves singular-value stability, while spatial separation remains most difficult for co-located LOS users. At 128 UCA antennas, measured-channel capacity reaches 50%–90% of the asymptotic capacity across the three scenarios.

  • Channel behavior: Sixteen users make spatial separation more difficult, producing larger singular value spreads than four-user cases in both measured and i.i.d. Rayleigh channels.The comparison applies across all three scenarios.
  • Channel behavior: Co-located LOS users have much larger measured-channel singular value spreads than i.i.d. Rayleigh channels, whereas NLOS conditions reduce the gap.Rich scattering in the NLOS scenario provides more favorable propagation for separating closely located users.
  • Channel behavior: Far-apart users produce measured-channel singular value-spread CDFs closer to i.i.d. Rayleigh channels, indicating improved spatial separation.This scenario includes users distributed across MS 1–8, with mixed LOS and NLOS conditions.
  • Capacity: 50% of the asymptotic capacity is achieved with 128 UCA antennas for co-located LOS users, compared with 75% for co-located NLOS and 90% for far-apart users.The asymptotic capacity for sixteen users is 55.4 bps/Hz, and the 128-antenna count is eight times the number of users.
  • Capacity: Despite more difficult separation with sixteen users, the UCA retains a large fraction of i.i.d. Rayleigh performance, especially in NLOS and far-apart-user conditions.Sixteen-user ULA measurements were unavailable, though higher ULA angular resolution is expected to help co-located users.

VI. SUMMARY AND CONCLUSIONS

The study uses measurements from practical and virtual 128-element arrays to examine massive MIMO across three real propagation scenarios. It finds that larger arrays improve channel orthogonality and stability, while measured-channel performance remains close to i.i.d. Rayleigh performance in the studied settings.

  • Study scope: Measurements with a practical UCA and virtual ULA, each having 128 elements, characterize massive MIMO in three representative propagation scenarios.The study evaluates singular value spreads and achieved sum-rate capacities.
  • Channel behavior: In all scenarios, increasing the antenna count considerably decreases and stabilizes singular value spreads over the measured bandwidth.The result indicates better orthogonality between channels to different users and improved channel stability.
  • Channel behavior: Co-located users with strong LOS have worse measured-channel user orthogonality than i.i.d. Rayleigh channels, yet still achieve a large fraction of the asymptotic capacity.This is identified as the most difficult studied situation.
  • Propagation conditions: NLOS rich scattering improves spatial separation for closely located users, while well-distributed users also improve performance.These are the more favorable propagation arrangements among the studied scenarios.
  • Conclusion: Measured channels with both the ULA and UCA achieve performance close to that in i.i.d. Rayleigh channels.This supports harvesting the theoretical advantages of massive MIMO in the studied real propagation environments.
Loading 1403.3376v3…